rocketry: achieving liftoff

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Rocketry: Achieving Liftoff



Outline

Forces on a Rocket Newton’s 1st and 2nd Laws of Motion Newton’s 3rd Law Combustion and Chemical Rockets Understanding Rocket Trajectories The Acceleration Phase The Descent Phase



1.1 Forces on a Rocket



Did you Know?

In order to reach orbit, NASA’s space shuttle must attain a speed of 7,847 meters per second (about 17,500 miles per hour).

How do rocket engines launch objects into space?



Forces Rocket engines are

able to move rockets at high speed because they apply a large amount of force to the rocket.

Forces are quantities known as vectors because they have both a magnitude and a direction.

Vectors are often drawn as arrows whose lengths indicate the magnitudes of the

forces.



Forces on Rockets

Thrust is the force created by the combustion of fuel that propels the rocket upward.

Drag is a force that results from the rocket pushing on the surrounding molecules of air. Drag is friction that acts in the direction opposite the motion of the rocket.

Weight is caused by gravity and pulls the rocket toward the ground.



Mass and Weight Mass and weight are not one and the same. Mass

measures the amount of matter in an object and does not vary from place to place. Weight measures the force of gravity on an object and varies depending on the strength of the gravity.

Weight can be represented as W = mg, where m is the mass of the object, and g is the acceleration due to gravity.



Powered Ascent There are three main phases of

rocket flight for rockets that do not enter orbit—powered ascent, coasting ascent, and descent.

Powered ascent occurs while the engine is producing thrust.

During powered ascent, T > W + D.



Coasting Ascent Coasting ascent happens after the

engine has stopped producing thrust.

During this phase, drag is very small compared to weight, so the force acting on the rocket is roughly equal to the weight.

The force of the weight causes the rocket to decelerate until its velocity reaches zero.

T = 0



Descent Descent occurs after the velocity of

the rocket reaches zero, at which point the rocket begins to accelerate toward the ground.

Most rockets have a parachute or other recovery system to increase drag until it balances the weight.

Increased drag slows the rocket down during descent.



Rocket Components A rocket consists of the rocket body,

the payload, the recovery system, and the engine, which includes the fuel.

The engine provides thrust and the recovery system increases drag.

The payloads of real rockets can include satellites, equipment, or people.



Example 1The mass of a model rocket body, payload, and recovery system is 34.0 g. The mass of the engine is 16.0 g. What is the weight of the rocket?First, we have to find the total mass of the rocket.

Next, we should convert the mass to kilograms, so that our solution for weight works out to be newtons.

Finally, we multiply the acceleration due to gravity (g) by mass to get weight.

m = 34.0 g+16.0 g = 50.0 g

1 kg= 50.0 g× = 0.05 kg

1,000 gm

2 2= 0.05 kg×9.81 m / s = 0.491 kg×m / s = 0.491 NW



1.2 Newton’s 1st and 2nd Laws



Newton’s 1st Law & Inertia

Newton’s first law of motion states that an object’s speed and direction of motion will remain unchanged unless an outside force acts on the object.

The tendency to resist changes in motion is a property of matter called inertia.



Newton’s 2nd Law & Acceleration

When a net force acts on an object and causes it to change its speed or its direction of motion, the object is said to be accelerated.

Newton’s 2nd law of motion states that to accelerate an object, we need to apply a force to the object.

Fnet = ma

Fnet = net force

m = mass

a = acceleration



Calculating AccelerationAcceleration is the change in speed of an object per unit of time, or the rate of change of an object’s speed.

1 0

1 0

v -va = =

t - t

change in speed

time



For any two objects with the same net force, Fnet, Newton’s 2nd Law requires that .

In other words, if you apply the same net force to two objects, and one of the objects has twice the mass of the other, the more massive object will accelerate only half as quickly as the less massive object.

1 2

2 1

a m=

a m

Newton’s 2nd Law



Exercise 1.3: Mass, Force, and Acceleration

Suppose you are performing acceleration experiments on two objects that have equal mass—a pillow and a shoe.If you accelerate the shoe twice as quickly as the pillow, how much more force do you need to apply to the shoe?

SOLUTIONNewton’s 2nd law of motion states that if the masses of two objects are the same, then the rate at which each object is accelerated is proportional to the net force. If the shoe is accelerated twice as quickly as the pillow, then the net force on the shoe is twice as large.



Rocket MotionAccording to Newton’s 2nd law, accelerating a rocket upward, or in a positive direction, requires a net upward force. The net forces acting on the rocket throughout its three phases of flight are as follows:

Launch and Powered Ascent: Fnet = T - W

Coasting Ascent: Fnet = - W

Descent: Fnet = D - W

*Notice that we always subtract W because it is always acting downward, or in a negative direction. Also, it is assumed that D 0 during ascent.



Example 4If a rocket has a mass of 50 g and the engine produces a thrust of 8 N at launch, what will be the initial acceleration of the rocket?

= 8.0N-0.491N = 7.51NnetF =T -W

2 227.51 N 7.51 kg×m / s 7.51 kg× m / s

= = = =150.2 m / s1 kg50 g 0.05 kg50 g×

1,000 g

netFa =

m

2

2

1 kg= 50 g× ×9.81 m / s

1,000 g

= 0.491 kg× m / s = 0.491 N

W = mg

Step 1: Solve for a by dividing both sides by m

Step 2: Find value of W

Step 3: Plug in numbers to find Fnet

Step 4: Simplify and convert to SI units

netF ma= = a

m m; therefore, netF

a =m



Activity 1.6: Testing Newton’s 2nd Law with a Rocket Car

Objective: You will conduct several trials to determine the effect of mass

on the time it takes your rocket car to travel a certain distance. In each trial, the net force applied to the car should be approximately the same.

Analysis:The travel time increases as mass is added to the car.

According to Newton’s 2nd law of motion, the more massive an object is, the more net force is required to accelerate it at a given rate.



2.1 Newton’s 3rd Law



Rocket Power

How do rocket engines propel aircraft? Or launch missiles from beneath the sea? Or launch spacecraft into orbit?

Like all propulsion systems, rocket engines generate thrust.

Thrust can be generated according to Newton’s 3rd law of motion.



Newton’s 3rd Law

Any force is always accompanied by a force of equal magnitude that acts in the opposite direction

In other words, the “action-reaction” principle

If you were standing on a skateboard and threw a ball, the ball would move forward

and you would move backward.



Conservation of Momentum

The final momentum of the system equals the initial momentum of the system, so the momentum of the system is conserved.

momentum = mass x velocity

MV = -mv

MV = momentum of person

mv = momentum of the ball



Putting it All Together

• Rocket engines and a person throwing a ball while standing on a skateboard generate thrust in a similar way.

• In rockets, the engine creates thrust by forcing propellant away from the rocket at high speed.

• This causes a reaction force (thrust) that pushes the rocket in the opposite direction.



Activity 2.4 Build a slingshot “car” that will demonstrate Newton’s 3rd law of

motion. Explain how Newton’s 3rd law relates to the behavior of your

slingshot car. How are the number of rubber bands and the amount of weight in the film canister related to the distance traveled by the car?

Answer: Even though the mass in the canister and the number of rubber bands varied, the action of launching the canister always occurred with the equal reaction of moving the car. When more rubber bands were added, the thrust force of the slingshot increased. When more mass was added to the film canister, the same amount of thrust would move the car farther.



2.2 Combustion and Chemical Rockets



Combustion

How does a rocket engine move the propellant away from the rocket at a high velocity?

Answer: A chemical reaction known as combustion

Fuel + Oxidizer → Products + Energy



Did you Know?The Saturn V rocket that launched the Apollo missions to the moon used liquid oxygen (LOX) as an oxidizer and a form of kerosene for fuel.



Energy for Propulsion

This figure illustrates the results of burning paper in a box. In the case of a rocket engine,

combustion of

the fuel and the oxidizer results in an extremely high gas pressure in the combustion chamber.



A Rocket Engine

In real rocket engines, the “box” where combustion takes place is called the combustion chamber.



A Model Rocket Engine

Model rocket engines (also called “motors”) are chemical rockets that use black powder as a propellant.



Activity 2.6Objective

Discover how Newton’s laws of motion determine the performance of a chemical rocket.

Materials

several sheets of construction paper, clear tape, scissors, paper towels, several effervescing antacid tablets, water, plastic 35 mm film canister, safety goggles, lab apron, paper towels for cleanup

Procedure

Record any observations you have on the performance of your rocket. Include an estimate of how high your rocket flew.

Repeat the experiment several times, each time changing one of the parameters of your rocket.



3.1 Understanding Rocket Trajectories



Three Phases

The path that a rocket takes while in flight is called a trajectory.

If the rocket doesn’t go into orbit, it completes three phases.

1. Powered ascent

2. Coasting ascent

3. Descent



Graph of a Rocket Trajectory

t

h

H

tb

Powered Ascent

Coasting Ascent

Descent

In a graph of height vs. time, constant acceleration is shown as a curved path called a parabola and constant velocity is shown as a straight line.



3.2 The Acceleration Phase



Predicting How Fast and How High

Maximum Velocity

Vb = velocity at burnout

I = impulse

Mavg = average rocket mass

g = acceleration caused by gravity

tb = engine burn time

Maximum Height

H = maximum height

g = acceleration caused by gravity

I = impulse

Mavg = average rocket mass

bavg

b gtM

IV

2

2

1

avgM

I

gH



Putting it All Together

The key factors that determine the maximum height and speed of a rocket are the engine impulse, the average mass of the rocket, and the engine burn time. Higher altitudes can be achieved by increasing the rocket’s impulse, by decreasing the burn time, or by decreasing the rocket’s average mass.



3.3 The Descent Phase



Importance of Drag

Unless a large drag is present during the descent phase, the rocket will fall at a high rate of speed and crash into the ground.

Parachutes and other types of recovery systems increase drag.



Drag Force

D = drag force

CD = drag coefficient

d = density of air

A = area of recovery system

VD = descent speed

CD for a parachute = 1.4

Objects like race cars and airplanes have low drag coefficients.

2

2

1DDdAVCD



Drag and a Parachute’s RadiusFor a parachute, A is the

area seen when looking straight up.

We can calculate area using A=πr2

The drag developed by the recovery system is determined by the shape of the recovery system (CD), its size (A), and the descent speed of the entire system.



Example 1After an Alpha III rocket with a B6-4 engine reaches a maximum altitude of 378 m at burnout, its parachute, with a diameter of 0.305 m, is deployed. The mass of the rocket, including its engine, is 53.1 g, and the mass of the propellant is 5.6 g. Assuming that the drag coefficient is 1.4 and the density of air is 1.20 kg/m3, how long will it take the rocket to reach the ground after the parachute is deployed?

Solution: First, calculate area of the parachute. Next, calculate the velocity, and finally, solve for the descent time. td = 2 min 15 sec

rocketry: achieving liftoff

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